Toroidal embeddings of cubic projective plane obstructions

TL;DR

This paper classifies how certain cubic graphs that cannot embed into the real projective plane can be embedded into the torus, providing a detailed understanding of their topological properties.

Contribution

It offers a complete classification of embeddings of cubic projective plane obstructions into the torus, extending previous work on topological minors.

Findings

Classified embeddings of cubic projective plane obstructions into the torus

Identified equivalence classes of these embeddings

Enhanced understanding of topological minors in graph embeddings

Abstract

Work of Glover and Huneke shows that a cubic graph embeds into the real projective plane if and only if it does not contain one of six topological minors called cubic projective plane obstructions. Here we classify up to equivalence the embeddings of these graphs into the torus.